A comparison of algorithms for control constrained optimal control of the Burgers equation

Abstract A comparison of three different but related numerical methods for control constrained optimal control of the Burgers equation is carried out. We develop the principal ideas of the different strategies considered and present detailed numerical examples. Lastly, conclusions about the behavior of the approaches are obtained.     

The effect of CaF<Subscript>2</Subscript> on thermodynamics of CaO-CaF<Subscript>2</Subscript>-SiO<Subscript>2</Subscript>(-MgO) slags

To address the role of CaF₂ in the CaO-CaF₂-SiO₂(-MgO) slag system employed for the production of low-pressure rotor steels, the thermodynamic aspects of the slag were investigated by equilibrating it with liquid iron at 1873 K in CaO or MgO crucibles. Presaturation of slag with an oxide block piece of CaO or MgO in a Pt crucible and application of a carbon paste to the outside of an oxide crucible were designed to prevent crucible failure during the slag-metal experiments. The liquidus isotherm and phase boundary of the preceding slag system were investigated using the slag-metal equilibria. Also, the effect of CaF₂ on the sulfide capacity and the activity coefficient of Fe _t O were of particular interest in controlling the sulfur level and cleanliness of low-pressure rotor steels.     

The transient to steady-state transition during the spray-rolling process

From the geometrical standpoint, this article presents a qualitative theoretical analysis and prediction of the transient to steady-state transition during the spray-rolling process, a novel manufacturing technique for aluminum strips. The analytical results indicate that, when the deposited materials at the specific points on one roll surface overlap their counterparts on the other roll surface, spray rolling transits from the transient state to the steady state. The specific points are the limiting deposition positions of the atomized droplets on the roll surface initially.     

Cyclic oxidation response of multiphase niobium-based alloys

Cyclic oxidation tests were performed on multiphase Nb-based alloys containing silicide, Laves, and Nb solid solution phases. In particular, the oxidation resistance of six alloys with various compositions (Nb, Ti, Hf, Cr, Ge, and Si) and microstructures was characterized by thermal cycling from ambient temperature to a peak temperature that ranges from 900 °C to 1400 °C. Weight change data were obtained and the corresponding spalled oxides were collected and identified by X-ray diffraction. The results indicated that Nb-based alloys formed a mixture of CrNbO₄, Nb₂O₅, and Nb₂O₅ · TiO₂, with possibly small amounts of SiO₂ or GeO₂. The oxidation resistance was improved when CrNbO₄ formed instead of Nb₂O₅ and Nb₂O₅ · TiO₂. These results were used to assess the influence of microstructure and composition on the oxidation resistance of multiphase Nb-based alloys.     

Kernel Spectral Matched Filter for Hyperspectral Imagery

In this paper a kernel-based nonlinear spectral matched filter is introduced for target detection in hyperspectral imagery, which is implemented by using the ideas in kernel-based learning theory. A spectral matched filter is defined in a feature space of high dimensionality, which is implicitly generated by a nonlinear mapping associated with a kernel function. A kernel version of the matched filter is derived by expressing the spectral matched filter in terms of the vector dot products form and replacing each dot product with a kernel function using the so called kernel trick property of the Mercer kernels. The proposed kernel spectral matched filter is equivalent to a nonlinear matched filter in the original input space, which is capable of generating nonlinear decision boundaries. The kernel version of the linear spectral matched filter is implemented and simulation results on hyperspectral imagery show that the kernel spectral matched filter outperforms the conventional linear matched filter.     

Preparation of clean coal by flotation following ultra fine liberation

This paper reports the results of current fundamental research at the Department of Process Engineering, University of Miskolc on the processing of clean coal from Mecsek bituminous coal, Southern Hungary. The theoretical possibility of the separation of different petrographic components was proven experimentally and their liberation degree was determined based on the petrographic composition, flotation kinetic study of isolated components (groups of components), scanning electron microscopy and microprobe analyses. The mill with stirred ball media was chosen for the ultra-fine liberation of the coal components. It was revealed that along with the liberation of coal components, their surface oxidation and spontaneous agglomeration, entrapping the mineral impurities take place in ultra-fine grinding. This paper discusses the interfacial phenomena occurring in the ultra-fine grinding process and their influence on the flotation. The concept for the advanced preparation of clean coal was developed, tested and proved. The main steps of this concept are the ultra-fine liberation in the stirred-media mill, the de-agglomeration of flocs spontaneously formed during the ultra-fine grinding and the induced (hydrophobic) flocculation with the following two-step flotation in a flotation column.     

Updated semi‐discretization method for periodic delay‐differential equations with discrete delay

An updated version of the semi‐discretization method is presented for periodic systems with a single discrete time delay. The delayed term is approximated as a weighted sum of two neighbouring discrete delayed state values and the transition matrix over a single period is determined. Stability charts are constructed for the damped and delayed Mathieu equation for different time‐period/time‐delay ratios. The convergence of the method is investigated by examples. Stability charts are constructed for 1 and 2 degree of freedom milling models. The codes of the algorithm are also attached in the appendix. Copyright © 2004 John Wiley & Sons, Ltd.     

Thomas Fincke und die <Emphasis Type="Italic">Geometria rotundi</Emphasis>

Thomas Fincke (January 6^th, 1561–April 24^th, 1656), born in Flensburg (Germany), was one of the very most important and significant scientists in Denmark during the seventeenth century, a mathematician and astrologer and physician in the beginning of modern science, a representative of humanism and an influentual academic organizer. He studied in Strasbourg (since 1577) and Padua (since 1583) and received his M.D. in Basel (1587), he practised as a physician throughout his life (since 1587 or 1590) and became a professor at Copenhagen (1591). But he was best known because of his Geometriae rotundi libri XIIII (1583), a famous book on plane and spherical trigonometry, based not on Euclid but on Petrus Ramus. In this influentual work, in which Fincke introduced the terms tangent and secant and probable first noticed the Law of Tangents and the so-called Newton-Oppel-Mauduit-Simpson-Mollweide-Gauss-formula, he showed himself to be „abreast of the mathematics of his time“.      

Fault-aware Communication Mapping for NoCs with Guaranteed Latency

As feature sizes shrink, transient failures of on-chip network links become a critical problem. At the same time, many applications require guarantees on both message arrival probability and response time. We address the problem of transient link failures by means of temporally and spatially redundant transmission of messages, such that designer-imposed message arrival probabilities are guaranteed. Response time minimisation is achieved by a heuristic that statically assigns multiple copies of each message to network links, intelligently combining temporal and spatial redundancy. Concerns regarding energy consumption are addressed in two ways. First, we reduce the total amount of transmitted messages, and, second, we minimise the application response time such that the resulted time slack can be exploited for energy savings through voltage reduction. The advantages of the proposed approach are guaranteed message arrival probability and guaranteed worst case application response time.